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Affine Tangles and Irreducible Exotic Sheaves

SPECIAL LECTURE

Topic:

Affine Tangles and Irreducible Exotic Sheaves

Speaker:

Rina Anno

Affiliation:

Harvard University

Date:

Tuesday, February 12

Time/Room:

2:00pm - 3:00pm/S-101

We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories $D_n$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element of $SL(2n)$ with two equal Jordan blocks. This representation allows us to enumerate the irreducible objects in the heart of the exotic $t$-structure on $D_n$ by crossingless matchings of $2n$ points on a circle. We also describe the algebra of endomorphisms of the direct sum of the irreducible objects. This algebra, as conjectured in 2006 by Paul Seidel, can be described as a variant of Khovanov's arc algebra.